Multimode Ultrastrong Coupling in Three-Dimensional Photonic-Crystal Cavities

TL;DR

This paper demonstrates multimode ultrastrong coupling in a three-dimensional photonic-crystal cavity at terahertz frequencies, revealing the importance of spatial mode profiles in exploring novel quantum electrodynamics phenomena.

Contribution

It reports the first realization of multimode ultrastrong coupling in 3D photonic-crystal cavities, supported by a multimode extended Hopfield model that considers spatial inhomogeneity.

Findings

Achieved multimode ultrastrong coupling in 3D-PCCs at terahertz frequencies

Experimental results match the extended Hopfield model considering spatial inhomogeneity

Discussed potential for strong ground-state correlations and nonintuitive quantum phenomena

Abstract

Recent theoretical studies have highlighted the role of spatially varying cavity electromagnetic fields in exploring novel cavity quantum electrodynamics (cQED) phenomena, such as the potential realization of the elusive Dicke superradiant phase transition. One-dimensional photonic-crystal cavities (PCCs), widely used for studying solid-state cQED systems, have uniform spatial profiles in the lateral plane. Three-dimensional (3D) PCCs, which exhibit discrete in-plane translational symmetry, overcome this limitation, but fabrication challenges have hindered the achievement of strong coupling in 3D-PCCs. Here, we report the realization of multimode ultrastrong coupling in a 3D-PCC at terahertz frequencies. The multimode coupling between the 3D-PCC's cavity modes and the cyclotron resonance of a Landau-quantized two-dimensional electron gas in GaAs is significantly influenced by the spatial profiles of the cavity modes, leading to distinct coupling scenarios depending on the probe polarization. Our experimental results are in excellent agreement with a multimode extended Hopfield model that accounts for the spatial inhomogeneity of the cavity field. Guided by the model, we discuss the possible strong ground-state correlations between different cavity modes and introduce relevant figures of merit for the multimode ultrastrong coupling regime. Our findings emphasize the importance of spatially nonuniform cavity mode profiles in probing nonintuitive quantum phenomena expected for the ground states of cQED systems in the ultrastrong coupling regime.